The amount of `._(6)C^(14)` isotope in a piece of wood is found to be one-fifth of that present in a fresh piece of wood. Calculate the age of wood (Half life of `C^(14) = 5577` years)

Explanation

To calculate the age of the wood based on the amount of Carbon-14 isotope present, we can follow these steps:

### Step 1: Understand the Problem
We know that the amount of Carbon-14 in the wood is one-fifth of that in a fresh piece of wood. We need to calculate the age of the wood using the half-life of Carbon-14, which is given as 5577 years.

### Step 2: Use the First-Order Decay Formula
For first-order decay, the relationship between the initial amount (A₀), the final amount (A), and time (t) is given by the formula:
\[ t = \frac{2.303}{\lambda} \log\left(\frac{A_0}{A}\right) \]
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